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Black holes generate collimated, relativistic jets, which have been observed in gamma-ray bursts (GRBs), microquasars, and at the center of some galaxies [active galactic nuclei (AGN)]. How jet physics scales from stellar black holes in GRBs to the supermassive ones in AGN is still unknown. Here, we show that jets produced by AGN and GRBs exhibit the same correlation between the kinetic power carried by accelerated particles and the gamma-ray luminosity, with AGN and GRBs lying at the low- and high-luminosity ends, respectively, of the correlation. This result implies that the efficiency of energy dissipation in jets produced in black hole systems is similar over 10 orders of magnitude in jet power, establishing a physical analogy between AGN and GRBs.